Mathematics, 26.11.2019 01:31 raekwon12

Asimple random sample of size 28 has mean x=7.26. g the population standard deviation is σ=3.72. the population is normally distributed. can you conclude that the population mean differs from 40? determine the parameter to be tested.

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Answer from: alyviariggins

Parameter tested: Population mean $\mu$

We have enough evidence to conclude that the population mean for this case differs from 40.

Step-by-step explanation:

1) Notation and definitions

n= 28 represent the sample size

/bar x =7.26 represent the sample mean obtained

$\sigma =3.72$ represent the population standard deviation known

$\mu_o =40$ the value that we want to compare or test

2) Concepts and formulas to use

The system of hypothesis that we need to check for this case are

Null Hypothesis: $\mu =40$

Alternative hypothesis: $\mu \neq 40$

We assume that the sample mean follows a normal distribution.

When conduct a Z test, to analyze if the population mean is equal to a apecified value $\mu_o =40$ :

In order to check the hypothesis we need to use the following statistic

$z=\frac{\bar X -\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

A one sample test of means "compares the mean of a sample to a prespecified value and tests for a deviation from that value".

Check for the assumptions that he sample must satisfy in order to apply the test

• The dependent variable must be continuous (interval/ratio). Satisfied

• The observations are independent of one another. We assume it.

• The dependent variable should be approximately normally distributed. Satisfied

• The dependent variable should not contain any outliers. We assume it.

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{7.26 -40}{\frac{3.72}{\sqrt{28}}}=-46.57$

4) Statistical decision

95% of the values in the normal standard distribution are between -1.96 and 1.96, if we obtain a value of z=-46.57, the p value for a two tailed test would be almost 0. And for this case at any significance level $\alpha$ we will reject the null hypothesis that the population mean is 40. So we have enough evidence to conclude that the population mean for this case differs from 40.

Answer from: Quest

17.08

correct me if i am wrong.

Answer from: Quest

middle maybe?

step-by-step explanation:

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